How to Calculate Cramer’s V in Python?

Cramer’s V: It is defined as the measurement of length between two given nominal variables. A nominal variable is a type of data measurement scale that is used to categorize the different types of data. Cramer’s V lies between 0 and 1 (inclusive). 0 indicates that the two variables are not linked by any relation. 1 indicates that there exists a strong association between the two variables. Cramer’s V can be calculated by using the below formula:

√(X²/N) / min(C-1, R-1)

Here, 

• X²: It is the Chi-square statistic
• N: It represents the total sample size
• R: It is equal to the number of rows
• C: It is equal to the number of columns

Example 1:

Let us calculate Cramer’s V for a 3 × 3 Table.

Python3

# Load necessary packages and functions
import scipy.stats as stats
import numpy as np

# Make a 3 x 3 table
dataset = np.array([[13, 17, 11], [4, 6, 9],
                    [20, 31, 42]])

# Finding Chi-squared test statistic,
# sample size, and minimum of rows
# and columns
X2 = stats.chi2_contingency(dataset, correction=False)[0]
N = np.sum(dataset)
minimum_dimension = min(dataset.shape)-1

# Calculate Cramer's V
result = np.sqrt((X2/N) / minimum_dimension)

# Print the result
print(result)

Output:

Output

The Cramers V comes out to be equal to 0.121 which clearly depicts the weak association between the two variables in the table.

Example 2: 

We will now calculate Cramer’s V for larger tables and having unequal dimensions. The Cramers V comes out to be equal to 0.12 which clearly depicts the weak association between the two variables in the table.

Python3

# Load necessary packages and functions
import scipy.stats as stats
import numpy as np

# Make a 5 x 4 table
dataset = np.array([[4, 13, 17, 11], [4, 6, 9, 12],
                    [2, 7, 4, 2], [5, 13, 10, 12],
                    [5, 6, 14, 12]])

# Finding Chi-squared test statistic,
# sample size, and minimum of rows and
# columns
X2 = stats.chi2_contingency(dataset, correction=False)[0]
N = np.sum(dataset)
minimum_dimension = min(dataset.shape)-1

# Calculate Cramer's V
result = np.sqrt((X2/N) / minimum_dimension)

# Print the result
print(result)

Output:

Output

The Cramers V comes out to be equal to 0.146 which clearly depicts the weak association between the two variables in the table.